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Dielectric response of spherical particles of graded materials
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Effective conductivity of composites of graded spherical particles
K. W. Yu1,2? and G. Q. Gu1,3
1Department of Physics, The Chinese University of Hong Kong,
Shatin, New Territories, Hong Kong
2Institute of Theoretical Physics, The Chinese University of Hong Kong,
Shatin, New Territories, Hong Kong
3College of Information Science and Technology, East China Normal University,
Shanghai 200 062, China
(February 1, 2008)
Abstract
We have employed the first-principles approach to compute the effective re-
sponse of composites of graded spherical particles of arbitrary conductivity
profiles. We solve the boundary-value problem for the polarizability of the
graded particles and obtain the dipole moment as well as the multipole mo-
ments. We provide a rigorous proof of an ad hoc approximate method based
on the differential effective multipole moment approximation (DEMMA) in
which the differential effective dipole approximation (DEDA) is a special case.
The method will be applied to an exactly solvable graded profile. We show
that DEDA and DEMMA are indeed exact for graded spherical particles.
PACS Number(s): 77.22.-d, 77.84.Lf, 42.79.Ry, 41.20.Cv
Typeset using REVTEX
?Corresponding author. Electronic mail: kwyu@phy.cuhk.edu.hk
1
I. INTRODUCTION
In functionally graded materials (FGM), the materials properties can vary spatially.
These materials have received considerable attention in various engineering applications [1].
The variation in the composition yields material and microstructure gradients, and makes the
FGM very different in behavior from the homogeneous materials and conventional composite
materials [1,2]. The great advantage is that one can tailor the materials properties via the
design of the gradients. Over the past few years, there have been a number of attempts, both
theoretical and experimental, to study the responses of FGM to mechanical, thermal, and
electr
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